A neural network solutions for routing in three stage interconnection networks

Abstract

A neural network solution to the problem of routing calls through a three-stage interconnection network is presented. The neural network is shown, via a theorem with proof, to select an open path through the interconnection network if one exists. The solution uses a Hopfield network with a binary threshold rather than a sigmoidal function. The weights of the neural network are fixed for all time, and thus are independent of the current state of the interconnection network. It is possible to implement various routing strategies through selection of inputs to the neural network, again independently of the weights. The convergence proof is based on a hypercube analysis technique that defines and locates all local minima of the neural network energy function. When one or more open paths exist, it is shown that all local minima correspond to such paths, and therefore convergence to a minimum is equivalent to selection of an open path. When no such path is available, the energy function is unimodal and the neural network converges to a null state indicating that the interconnection network is blocked. >